Does the table represent a proportional relationship
X 3/4 , 3/8, 3/10, 3/14
Y 1/2 ,1/4, 1/5, 1/7
A. No because all numbers are positive
B. Yes, because the ratios of y and x are equal to 2/3
C. No, because the ratios of y to x are not all equal
D. Yes, because the ratios of y to x are all equal to 1/3
C. No, because the ratios of y to x are not all equal.
To determine if the table represents a proportional relationship, we need to check if the ratios of y to x are equal for all values. Let's calculate the ratios:
For the first row: y/x = (1/2) / (3/4) = (1/2) * (4/3) = 2/3
For the second row: y/x = (1/4) / (3/8) = (1/4) * (8/3) = 2/3
For the third row: y/x = (1/5) / (3/10) = (1/5) * (10/3) = 2/3
For the fourth row: y/x = (1/7) / (3/14) = (1/7) * (14/3) = 2/3
Since the ratios of y to x are all equal to 2/3, the answer is:
B. Yes, because the ratios of y and x are equal to 2/3
To determine if the table represents a proportional relationship, we need to check if the ratios of y to x are equal for all values.
To do this, we can calculate each ratio and compare them:
1. For the first pair of values:
y/x = (1/2) / (3/4) = (1/2) * (4/3) = 2/3
2. For the second pair of values:
y/x = (1/4) / (3/8) = (1/4) * (8/3) = 1/6
3. For the third pair of values:
y/x = (1/5) / (3/10) = (1/5) * (10/3) = 2/15
4. For the fourth pair of values:
y/x = (1/7) / (3/14) = (1/7) * (14/3) = 2/21
As you can see, the ratios of y to x (in simplified form) are not all equal.
Therefore, the answer is C. No, because the ratios of y to x are not all equal.